Which of the following contains maximum number of molecules?

Options

A. 1 g `N_(2)`
B. 1 g `CO_(2)`
C. 1 g `H_(2)`
D. 1g `O_(2)`

Explanation

To find out which of the given options contains the maximum number of molecules, we will calculate the number of molecules in each substance based on the provided mass (1 gram) and their respective molar masses.

### Step-by-Step Solution:

1. **Identify the Molar Masses:**
- For \( N_2 \) (Nitrogen gas):
- Molar mass = \( 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \)
- For \( CO_2 \) (Carbon dioxide):
- Molar mass = \( 12 \, \text{g/mol} + (16 \, \text{g/mol} \times 2) = 44 \, \text{g/mol} \)
- For \( H_2 \) (Hydrogen gas):
- Molar mass = \( 1 \, \text{g/mol} \times 2 = 2 \, \text{g/mol} \)
- For \( O_2 \) (Oxygen gas):
- Molar mass = \( 16 \, \text{g/mol} \times 2 = 32 \, \text{g/mol} \)

2. **Calculate the Number of Molecules:**
- Use Avogadro's number \( N_a = 6.022 \times 10^{23} \, \text{molecules/mol} \) to find the number of molecules in 1 gram of each gas.
- For \( N_2 \):
\[ \text{Number of molecules} = \frac{N_a}{28} = \frac{6.022 \times 10^{23}}{28} \]
- For \( CO_2 \):
\[ \text{Number of molecules} = \frac{N_a}{44} = \frac{6.022 \times 10^{23}}{44} \]
- For \( H_2 \):
\[ \text{Number of molecules} = \frac{N_a}{2} = \frac{6.022 \times 10^{23}}{2} \]
- For \( O_2 \):
\[ \text{Number of molecules} = \frac{N_a}{32} = \frac{6.022 \times 10^{23}}{32} \]

3. **Calculate Each Value:**
- For \( N_2 \):
\[ \frac{6.022 \times 10^{23}}{28} \approx 2.15 \times 10^{22} \, \text{molecules} \]
- For \( CO_2 \):
\[ \frac{6.022 \times 10^{23}}{44} \approx 1.37 \times 10^{22} \, \text{molecules} \]
- For \( H_2 \):
\[ \frac{6.022 \times 10^{23}}{2} \approx 3.01 \times 10^{23} \, \text{molecules} \]
- For \( O_2 \):
\[ \frac{6.022 \times 10^{23}}{32} \approx 1.88 \times 10^{22} \, \text{molecules} \]

4. **Compare the Number of Molecules:**
- \( N_2 \): \( 2.15 \times 10^{22} \)
- \( CO_2 \): \( 1.37 \times 10^{22} \)
- \( H_2 \): \( 3.01 \times 10^{23} \)
- \( O_2 \): \( 1.88 \times 10^{22} \)

5. **Conclusion:**
- The maximum number of molecules is found in \( H_2 \) (Hydrogen gas) with approximately \( 3.01 \times 10^{23} \) molecules.

### Final Answer:
The option that contains the maximum number of molecules is **\( H_2 \)**.